Evaluate
\frac{770500}{127907}\approx 6.023907996
Factor
\frac{2 ^ {2} \cdot 5 ^ {3} \cdot 23 \cdot 67}{13 \cdot 9839} = 6\frac{3058}{127907} = 6.023907995653092
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\begin{array}{l}\phantom{1023256)}\phantom{1}\\1023256\overline{)6164000}\\\end{array}
Use the 1^{st} digit 6 from dividend 6164000
\begin{array}{l}\phantom{1023256)}0\phantom{2}\\1023256\overline{)6164000}\\\end{array}
Since 6 is less than 1023256, use the next digit 1 from dividend 6164000 and add 0 to the quotient
\begin{array}{l}\phantom{1023256)}0\phantom{3}\\1023256\overline{)6164000}\\\end{array}
Use the 2^{nd} digit 1 from dividend 6164000
\begin{array}{l}\phantom{1023256)}00\phantom{4}\\1023256\overline{)6164000}\\\end{array}
Since 61 is less than 1023256, use the next digit 6 from dividend 6164000 and add 0 to the quotient
\begin{array}{l}\phantom{1023256)}00\phantom{5}\\1023256\overline{)6164000}\\\end{array}
Use the 3^{rd} digit 6 from dividend 6164000
\begin{array}{l}\phantom{1023256)}000\phantom{6}\\1023256\overline{)6164000}\\\end{array}
Since 616 is less than 1023256, use the next digit 4 from dividend 6164000 and add 0 to the quotient
\begin{array}{l}\phantom{1023256)}000\phantom{7}\\1023256\overline{)6164000}\\\end{array}
Use the 4^{th} digit 4 from dividend 6164000
\begin{array}{l}\phantom{1023256)}0000\phantom{8}\\1023256\overline{)6164000}\\\end{array}
Since 6164 is less than 1023256, use the next digit 0 from dividend 6164000 and add 0 to the quotient
\begin{array}{l}\phantom{1023256)}0000\phantom{9}\\1023256\overline{)6164000}\\\end{array}
Use the 5^{th} digit 0 from dividend 6164000
\begin{array}{l}\phantom{1023256)}00000\phantom{10}\\1023256\overline{)6164000}\\\end{array}
Since 61640 is less than 1023256, use the next digit 0 from dividend 6164000 and add 0 to the quotient
\begin{array}{l}\phantom{1023256)}00000\phantom{11}\\1023256\overline{)6164000}\\\end{array}
Use the 6^{th} digit 0 from dividend 6164000
\begin{array}{l}\phantom{1023256)}000000\phantom{12}\\1023256\overline{)6164000}\\\end{array}
Since 616400 is less than 1023256, use the next digit 0 from dividend 6164000 and add 0 to the quotient
\begin{array}{l}\phantom{1023256)}000000\phantom{13}\\1023256\overline{)6164000}\\\end{array}
Use the 7^{th} digit 0 from dividend 6164000
\begin{array}{l}\phantom{1023256)}0000006\phantom{14}\\1023256\overline{)6164000}\\\phantom{1023256)}\underline{\phantom{}6139536\phantom{}}\\\phantom{1023256)99}24464\\\end{array}
Find closest multiple of 1023256 to 6164000. We see that 6 \times 1023256 = 6139536 is the nearest. Now subtract 6139536 from 6164000 to get reminder 24464. Add 6 to quotient.
\text{Quotient: }6 \text{Reminder: }24464
Since 24464 is less than 1023256, stop the division. The reminder is 24464. The topmost line 0000006 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 6.
Examples
Quadratic equation
{ x } ^ { 2 } - 4 x - 5 = 0
Trigonometry
4 \sin \theta \cos \theta = 2 \sin \theta
Linear equation
y = 3x + 4
Arithmetic
699 * 533
Matrix
\left[ \begin{array} { l l } { 2 } & { 3 } \\ { 5 } & { 4 } \end{array} \right] \left[ \begin{array} { l l l } { 2 } & { 0 } & { 3 } \\ { -1 } & { 1 } & { 5 } \end{array} \right]
Simultaneous equation
\left. \begin{cases} { 8x+2y = 46 } \\ { 7x+3y = 47 } \end{cases} \right.
Differentiation
\frac { d } { d x } \frac { ( 3 x ^ { 2 } - 2 ) } { ( x - 5 ) }
Integration
\int _ { 0 } ^ { 1 } x e ^ { - x ^ { 2 } } d x
Limits
\lim _{x \rightarrow-3} \frac{x^{2}-9}{x^{2}+2 x-3}